We study the problem of computing possible and necessary winners for partially specified weighted and unweighted tournaments. This problem arises naturally in elections with incompletely specified votes, partially completed sports competitions, and more generally in any scenario where the outcome of some pairwise comparisons is not yet fully known. We specifically consider a number of well-known solution concepts---including the uncovered set, Borda, ranked pairs, and maximin---and show that for most of them, possible and necessary winners can be identified in polynomial time. These positive algorithmic results stand in sharp contrast to earlier results concerning possible and necessary winners given partially specified preference profiles.

Fuzzy c-neural network models (FCNNM) combine clustering techniques with advanced neural networks for time series modeling in order to make predictions for a possibly large set of time series using only a small number of models. Given a set of time series, FCNNM finds a partition matrix that quantifies to which degree each time series is associated with each prediction model, as well as the parameters of the neural network models for each cluster. FCNNM allows to automatically identify groups of time series with similar dynamics. This results in higher data efficiency, being of particular interest in cases of poor data availability. We illustrate the application of FCNNM to cash withdrawal series as part of an effective cash management.

Fuzzy c-auto regression models (FCARM) combine clustering with time series prediction. Given a set of time series, FCARM finds clusters of time series with similar dynamics. More specifically, FCARM finds a partition matrix that quantifies to which degree each time series is associated with each prediction model, and the parameters of the (linear) auto regression models for each cluster. FCARM can thus be used for two different purposes: (i) the automatic identification of clusters of time series with similar dynamics and (ii) the forecast of a large number of time series using only a small number of generic forecast models, leading to higher data efficiency and lower model validation and maintenance effort. We illustrate the application of FCARM to sales forecasts for products that can be clustered into groups with similar sales dynamics.